The diffraction of harmonic plane waves at a perfectly conducting half
-plane leads to a Dirichlet or Neumann problem for the two-dimensional
(2D) Helmholtz equation. As proved by Bateman the solution may be exp
ressed in terms of Weber functions. We first prove that his result can
be generalized to a perfectly conducting wedge. Then, assuming that t
he electromagnetic properties of a diffracting obstacle can be describ
ed by a surface impedance we analyze the diffraction at nonperfectly c
onducting planes and wedges; this corresponds to a mixed boundary valu
e problem for the 2D Helmholtz equation.